12,903 research outputs found
Belief Revision, Minimal Change and Relaxation: A General Framework based on Satisfaction Systems, and Applications to Description Logics
Belief revision of knowledge bases represented by a set of sentences in a
given logic has been extensively studied but for specific logics, mainly
propositional, and also recently Horn and description logics. Here, we propose
to generalize this operation from a model-theoretic point of view, by defining
revision in an abstract model theory known under the name of satisfaction
systems. In this framework, we generalize to any satisfaction systems the
characterization of the well known AGM postulates given by Katsuno and
Mendelzon for propositional logic in terms of minimal change among
interpretations. Moreover, we study how to define revision, satisfying the AGM
postulates, from relaxation notions that have been first introduced in
description logics to define dissimilarity measures between concepts, and the
consequence of which is to relax the set of models of the old belief until it
becomes consistent with the new pieces of knowledge. We show how the proposed
general framework can be instantiated in different logics such as
propositional, first-order, description and Horn logics. In particular for
description logics, we introduce several concrete relaxation operators tailored
for the description logic \ALC{} and its fragments \EL{} and \ELext{},
discuss their properties and provide some illustrative examples
Modeling of Phenomena and Dynamic Logic of Phenomena
Modeling of complex phenomena such as the mind presents tremendous
computational complexity challenges. Modeling field theory (MFT) addresses
these challenges in a non-traditional way. The main idea behind MFT is to match
levels of uncertainty of the model (also, problem or theory) with levels of
uncertainty of the evaluation criterion used to identify that model. When a
model becomes more certain, then the evaluation criterion is adjusted
dynamically to match that change to the model. This process is called the
Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes
of the mind and natural evolution. This paper provides a formal description of
DLP by specifying its syntax, semantics, and reasoning system. We also outline
links between DLP and other logical approaches. Computational complexity issues
that motivate this work are presented using an example of polynomial models
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